(28x-7)(24x+18)=180

Solution for (28x-7)(24x+18)=180 equation:

Simplifying
(28x + -7)(24x + 18) = 180

Reorder the terms:
(-7 + 28x)(24x + 18) = 180

Reorder the terms:
(-7 + 28x)(18 + 24x) = 180

Multiply (-7 + 28x) * (18 + 24x)
(-7(18 + 24x) + 28x * (18 + 24x)) = 180
((18 * -7 + 24x * -7) + 28x * (18 + 24x)) = 180
((-126 + -168x) + 28x * (18 + 24x)) = 180
(-126 + -168x + (18 * 28x + 24x * 28x)) = 180
(-126 + -168x + (504x + 672x2)) = 180

Combine like terms: -168x + 504x = 336x
(-126 + 336x + 672x2) = 180

Solving
-126 + 336x + 672x2 = 180

Solving for variable 'x'.

Reorder the terms:
-126 + -180 + 336x + 672x2 = 180 + -180

Combine like terms: -126 + -180 = -306
-306 + 336x + 672x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-306 + 336x + 672x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-51 + 56x + 112x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-51 + 56x + 112x2)' equal to zero and attempt to solve:

Simplifying
-51 + 56x + 112x2 = 0

Solving
-51 + 56x + 112x2 = 0

Begin completing the square.  Divide all terms by
112 the coefficient of the squared term: 

Divide each side by '112'.
-0.4553571429 + 0.5x + x2 = 0

Move the constant term to the right:

Add '0.4553571429' to each side of the equation.
-0.4553571429 + 0.5x + 0.4553571429 + x2 = 0 + 0.4553571429

Reorder the terms:
-0.4553571429 + 0.4553571429 + 0.5x + x2 = 0 + 0.4553571429

Combine like terms: -0.4553571429 + 0.4553571429 = 0.0000000000
0.0000000000 + 0.5x + x2 = 0 + 0.4553571429
0.5x + x2 = 0 + 0.4553571429

Combine like terms: 0 + 0.4553571429 = 0.4553571429
0.5x + x2 = 0.4553571429

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 0.4553571429 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 0.4553571429 + 0.0625

Combine like terms: 0.4553571429 + 0.0625 = 0.5178571429
0.0625 + 0.5x + x2 = 0.5178571429

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 0.5178571429

Calculate the square root of the right side: 0.719622917

Break this problem into two subproblems by setting 
(x + 0.25) equal to 0.719622917 and -0.719622917.

Subproblem 1
x + 0.25 = 0.719622917

Simplifying
x + 0.25 = 0.719622917

Reorder the terms:
0.25 + x = 0.719622917

Solving
0.25 + x = 0.719622917

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 0.719622917 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 0.719622917 + -0.25
x = 0.719622917 + -0.25

Combine like terms: 0.719622917 + -0.25 = 0.469622917
x = 0.469622917

Simplifying
x = 0.469622917

Subproblem 2
x + 0.25 = -0.719622917

Simplifying
x + 0.25 = -0.719622917

Reorder the terms:
0.25 + x = -0.719622917

Solving
0.25 + x = -0.719622917

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -0.719622917 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -0.719622917 + -0.25
x = -0.719622917 + -0.25

Combine like terms: -0.719622917 + -0.25 = -0.969622917
x = -0.969622917

Simplifying
x = -0.969622917

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.469622917, -0.969622917}
Solution
x = {0.469622917, -0.969622917}